As a Jeopardy second-placer (but, in my defense, to a 5-time champ on her fifth day), I second what everyone else here has said. Brush up on easy factual categories like Presidents, capitals – I had my son drill me on US, Canadian, and Australian state/provincial capitals as well as world capitals – and categories like opera or mythology that a quick refresher on will give you enough info for an average game.
But for the written test itself, what worked for me was to try to note down questions I knew as fast as possible, and for ones I didn’t know, to write a one or two-word hint to myself of what it was about. So during the times when I’d have a question answered before Alex even finished reading it on the tape of the test, that would give me ten seconds or so to go back and fill in a blank or three. It paid off.
Then, once you pass the test, you do the mock game tryout. They can get thousands of people who can answer every question in the world; they want people who are good on TV, who are personable, gracious losers, and fun to watch. So definitely show some personality and look like you are having fun. People watching you will have fun if you are.
That’s what they told me, too, but they never did ask me again when I got to LA – they just told me, “Oh, we have all that from your test.” Which was not at all the things I would have put down had I had a chance to think about it, so I made a pain of myself and insisted on them editing my info to get it right. They wouldn’t have if I hadn’t insisted. So go in with it planned. If you win like Ken, however, you’re on your own!
Most of all, have fun, and if at first you don’t succeed, keep trying. It took me two tries to pass, and lots of successful players have tried multiple times, so an initial failure isn’t the kiss of death.